References & Citations

Bookmark

Mathematical Physics

Title:Rigorous Formulation of Duality in Gravitational Theories

Abstract: In this paper we evince a rigorous formulation of duality in gravitational
theories where an Einstein like equation is valid, by providing the conditions
under which the Hodge duals (with respect to the metric tensor g) of T^a and
R_b^a may be considered as the torsion and curvature 2-forms associated with a
connection D', part of a Riemann-Cartan structure (M,g',D'), in the cases g =
g' and g does not equal g', once T^a and R_b^a are the torsion and curvature
2-forms associated with a connection D part of a Riemann-Cartan structure
(M,g,D). A new form for the Einstein equation involving the dual of the Riemann
tensor of D is also provided, and the result is compared with others appearing
in the literature.